An algebra problem by Nikko Quirap

Algebra Level 5

Suppose that the tires on the rear of your brand new Hilux will wear out after 33 600 kilometers, whereas tires on the front will wear out after 46 400 kilometers. Also, suppose that five identical tires, including the spare, come with the car. If yo can easily change the tires whenever yo want, what is the maximum distance you can drive?


The answer is 48720.

Nikko Quirap by Nikko Quirap , 24, Philippines

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3 solutions

Sahil Gohan
Apr 12, 2014

1) the tire's wear in the ratio 46400/33600 = 29/21

2) let life of 1 Tyre be x. we have 5 tires so their combined life is 5x. we have to divide this combined life in the ratio 29/21

3) (5x / 50) * 21 * 46400 = 2.1(x) * 46400 is the amount both the front tire's will travel.

which is 97440.since we have to find for individual tire it will be 97440/2 = 48720

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Nikko Quirap
Apr 2, 2014

So the maximum number of kilometers that can be driven occurs when we spread the thread wear evenly among the five tires. That is, the maximum number of kilometers that we can driven is 2/(33 600)+2/(46 400) If we assume that the thread wear rate is a linear function of kilometers driven, the total thread wear per kilometers is 5/(2/(33 600)+2/(46 400))=5/(2/100 ( 1/336+1/464) ) 250/(25/(4 872))=48 720 km

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Did it the same way

saptarshi dasgupta - 4 years, 1 month ago

For ever 50000 on front and 50000 km on rear, that is total 100000 km the wear for each is is 50000/33600 + 500000/46400 = 2.5658. thus km for unity wear is 100000/2.5658. But we sue only 4 at a time , the fifth can run one forth of it so to say.

Thus the five will run 5/4*(100000/2.5658) = 48720 km.

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